Wave Turbulence of Capillary Waves in Finite Systems

We consider classical problem of turbulence of capillary waves. In a series of numerical simulations it is shown that Zakharov-Filonenko spectrum corresponding to direct cascade of energy has a limited dynamic range of realization in a finite system, which shrinks with decreasing level of nonlinearity. Recent hypothesis that this dynamic range scales with average steepness as $\simμ^{8/3}$ is confirmed. As a byproduct the Zakharov-Filonenko spectrum was observed for record dynamic range close to or beyond one decade in a variety of simulation configurations.